High-Low Promotion Policies for Peak-End Demand Models
Bibliographic record
Abstract
In-store promotions are a highly effective marketing tool that can have a significant impact on revenue. In this research, we study the question of dynamic promotion planning in the face of Bounded-Memory Peak-End demand models. In order to determine promotion strategies, we establish that a High-Low pricing policy is optimal under diagonal dominance conditions (so that the current period price dominates both past period price effects and competitive product price effects on the demand), as well as conditions on the price dispersion. We show that finding the optimal High-Low dynamic promotion policy is NP-hard in the strong sense. Nevertheless, for the special case of promotion planning for a single item, we propose a compact Dynamic Programming (DP) approach that can find the optimal promotion plan that follows a High-Low policy in polynomial time. When the diagonal dominance conditions do not hold, and, hence, a High-Low policy is not necessarily optimal, we show that the optimal High-Low policy that is found by our proposed DP can find a provably near-optimal solution. Using the proposed DP as a subroutine, for the case of multiple items, we propose a Polynomial-Time-Approximation Scheme (PTAS) that can find a solution that can capture at least [Formula: see text] of the optimal revenue and runs in time that is exponential only in [Formula: see text]. Finally, we test our approach on data from large retailers and demonstrate an average of [Formula: see text] increase in revenue relative to the retailer’s current practices. This paper was accepted by Chung Piaw Teo, optimization. Funding: Financial support from the Oracle Corporation [External Research Office grant] and the National Science Foundation [Grant CMMI-1162034] is gratefully acknowledged.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".